Technical Background - Computer Animation: Algorithms and Techniques - page 34

y

y

z

x

A

x

B

z

FIGURE 2.1
(a) Left-handed and (b) right-handed coordinate systems.

of matrices, representing compound transformations in a matrix, and extracting a series of basic
transformations from a compound matrix. The display pipeline is then described in terms of the trans-
formation matrices used to affect it; the discussion is focused on transforming a point in space. In the
case of transforming vectors, the computation is slightly different (see Appendix B.3.2 for details).
This section concludes with a discussion of error considerations, including orthonormalization of a
rigid transformation matrix. Unless stated otherwise, space is assumed to be three-dimensional and
right-handed.

2.1.1 The display pipeline
The display pipeline refers to the transformation of object data from its original defining space through
a series of intermediate spaces until its final mapping onto the screen. The object data are transformed
into different spaces in order to efficiently compute illumination, clip the data to the view volume, and
perform the perspective transformation. This section reviews these spaces, their properties, the trans-
formations that map data from one space to the next, and the parameters used to specify the transfor-
mations. The names used for these spaces vary from text to text, so they will be reviewed here to
establish a consistent naming convention for the rest of the topic. While an important process that
eliminates lines and parts of lines that are not within the viewable space, clipping is not relevant to
motion control and therefore is not covered.
The space in which an object is originally defined is referred to as object space . The data in object
space are usually centered at the origin and often are created to lie within some limited standard range
such as 1. The object, as defined by its data points (which are also referred to as its vertices ),

is transformed, usually by a series of rotations, translations, and scales, into world space , the space in
which objects are assembled to create the environment to be viewed. Object space and world space are
commonly right-handed spaces.
World space is also the space in which light sources and the observer are placed. For purposes of
this discussion, observer position is used synonymously and interchangeably with camera position and
eye position . The observer parameters include its position and its orientation . The orientation is fully
specified by the view direction and the up vector . There are various ways to specify these orientation
vectors. Sometimes the view direction is specified by giving a center of interest (COI), in which case
the view direction is the vector from the observer or eye position (EYE) to the center of interest.
The eye position is also known as the look-from point , and the COI is also known as the look-to point .
The default orientation of “straight up” is defined as the observer's up vector being perpendicular to the

1to þ